Solution: 2014 Fall Final - 8

Author: Michiel Smid

Question

The number of different strings that can be made by reordering the 10 letters of the word AAABBCCCCC is

(a)

None of the above.

(b)

${10 \choose 3}{10 \choose 2}{10 \choose 5}$

(c)

$10!$

(d)

$\frac{10!}{2!3!5!}$

$ \binom{10}{3} \cdot \binom{7}{2} \cdot \binom{5}{5} $

$ = \frac{10!}{3!7!} \cdot \frac{7!}{2!5!} \cdot \frac{5!}{5!0!} $

$ = \frac{10!}{3!1} \cdot \frac{1}{2!5!} \cdot \frac{1}{1 \cdot 1} $

$ = \frac{10!}{3!2!5!} $